Quasistatic stopband in the spectrum of one-dimensional piezoelectric phononic crystal

TL;DR

This paper investigates how a negative capacitance in a piezoelectric phononic crystal can create a quasistatic stopband at zero frequency, revealing unique spectral features like infinite group velocity and flat bands.

Contribution

It demonstrates the existence of a quasistatic absolute stopband in a one-dimensional piezoelectric phononic crystal when the circuit capacitance is negative, a novel spectral phenomenon.

Findings

Quasistatic stopband appears at zero frequency for negative capacitance C<0.

Spectrum exhibits infinite group velocity at the origin for certain parameters.

Flat bands occur at specific fixed negative capacitance values.

Abstract

Propagation of a longitudinal wave through the periodic structure composed of alternating elastic and piezoelectric layers is considered. The faces of each piezoelectric layer are electroded and connected via a circuit with the capacity $C$. It is shown that if $C<0$ then the Floquet-Bloch spectrum $ \omega(K)$ in a certain range of negative $C$ may possess a quasistatic absolute stopband starting at $\omega =0$. Other unusual features of the spectrum occurring at certain fixed values of $C<0$ are the infinite group velocity of the first branch at the origin point $\omega =0$, $K=0$ and the flat bands $\omega={\rm const}$.